In 1976, Christopherson co-founded the massively influential London electronic music and avant-garde performance art crew Throbbing Gristle, one of a handful of groups who helped create industrial music. The group was famous for confrontational, intense performances, with frontman Genesis P-Orridge presenting an art exhibit of used tampons and diapers at their very first show, according to Allmusic. But they were also a musical force, releasing the classic album 20 Jazz Funk Greats in 1979. Their independent record label, Industrial Records, helped pioneer the DIY punk movement.

The group broke up for the first time in 1981, with Christopherson and P-Orridge going on to form the similarly demented Psychic TV soon after. In 1983, Christopherson left that group, teaming up with his partner, Jhonn Balance (also a veteran of Psychic TV) to form the industrial duo Coil. Coil were influential in their own right; Trent Reznor's new group How to Destroy Angels took their name from a 1984 Coil EP. Coil ended in 2004 when Balance died. In the years that followed, Christopherson moved to Thailand and launched two music projects, the Threshold HouseBoys Choir and Soisong.

In 2009, Throbbing Gristle launched a well-received reunion tour. Earlier this month, P-Orridge abruptly left the group, with the remaining members announcing plans to continue on under the name X-TG. (P-Orridge later disputed the other members' claims about the exit, writing, "We want to make it clear right now that we did not, and have no wish to quit TG. Obviously there is more involved than just that simple statement.")

A visual artist as well as a musician, Christopherson worked for the pioneering design agency Hipgnosis, who did cover art for groups like Led Zeppelin and Pink Floyd. He also took the first promo photos of the Sex Pistols.

In the note on the Throbbing Gristle website, members Cosey Fanni Tutti and Chris Carter write, "The music and art world has lost a great talent whose unique approach ignored the conventions of the day and often challenged the status quo... Sleazy was a kind and beautiful soul. No words can express how much he will be missed."